A prospect of noninvasive mapping of the electrical properties of tissues and materials has long been contemplated by scientists. “Electrical prospection” techniques have a long and rich history, in which a panoply of probes and innovative algorithms have been brought to bear in an attempt to solve the inherently ill-conditioned inverse problem associated with deducing internal electrical property maps from nondestructive external measurements. Despite the intrinsic difficulty of the problem and the absence of widespread successes with broad utilization so far, strong interest has persisted to the present day. This is likely because robust determination of the spatial distribution of electrical conductivity and permittivity would enable a wide range of applications in a similarly wide range of fields, from materials science to clinical diagnostics.
In the area of materials science, noninvasive mapping of the electrical properties of materials would expand the capabilities of nondestructive testing, with potential applications in manufacturing, geology, archaeology, forensics, etc. Meanwhile, in the biomedical arena, the visualization of localized changes in conductivity and permittivity could provide biophysical information complementary to that available from currently available imaging modalities such as Magnetic Resonance Imaging (MRI), Computed Tomography (CT), or ultrasound. Magnetoencephalography or electrocardiography can track intrinsic electrical activity in the brain or the heart, albeit at coarse spatial resolution; however, these modalities do not provide direct information about the electrical substrate of otherwise passive tissues. Indeed, all tissues are electromagnetic entities, with varying abilities to carry currents and store charges. Current-carrying and charge-storage capacities represent fundamental properties of the tissue microenvironment which might be expected to provide valuable information about disease processes, e.g. involving membrane derangements, muscle dysfunction, fluid accumulation, etc. It is known from invasive measurements that the electrical properties of tumors can differ dramatically from those of healthy tissue, making cancer a prominent target for early testing of techniques such as Electrical Impedance Tomography (EIT). Moreover, knowledge of the spatial distribution of electrical conductivity and permittivity would be valuable as a practical adjunct for various existing diagnostic and therapeutic technologies. The ability of heterogeneous tissues to respond to externally applied electromagnetic fields can dictate the success of therapeutic interventions such as transcranial magnetic stimulation or radiofrequency ablation. Interactions of electromagnetic fields with the body can distort images obtained with high-field MRI scanners, limiting the practical use of these powerful devices. Knowledge of electrical properties could be used to correct these distortions.
Previous approaches to electrical property mapping, also commonly referred to as electrical impedance imaging, may be classified according to two complementary criteria: a) use of injected currents versus applied fields, and b) reliance upon surface measurements versus interior data. EIT represents the canonical surface-based technique using injected currents. Alternative surface-based techniques which avoid direct application of currents include Microwave Tomography (MWT) and Magnetic Induction Tomography (MIT), as well as less well-known techniques such as noise tomography and Radiofrequency Impedance Mapping (RFIM). All such electrical prospection techniques utilize the solution of ill-posed inverse problems, which carry with them fundamental challenges of robustness, spatial resolution, etc. Once it was recognized that MRI may be used as a probe of the internal distribution of currents and magnetic fields, however, new techniques for impedance mapping began to emerge, including the injected-current-based MREIT approach, and the field-based electrical properties tomography (EPT) technique. These techniques circumvent the fundamental limitations of surface-based inverse problems, but they must contend with the fact that MRI generally provides only partial information about interior currents and fields.
The EPT technique, for example, achieves noninvasive electrical property mapping without injected currents by manipulating maps of RF transmitter sensitivity and MR signal phase. Results with EPT to date have been promising, with early in vivo studies in patient populations just emerging. However, EPT suffers from a fundamental lack of access to absolute RF phase, as all measurable phases are expressed in relation to some unknown reference phase distribution. This limitation has for many years been considered inescapable—a basic feature of the elementary processes by which we detect magnetic resonance signals. EPT circumvents this limitation to some extent by using a carefully-chosen coil design (a birdcage) and associated symmetry assumptions dictating field behavior in the body. However, these assumptions generally fail preferentially at high field strength—precisely where field curvature is greatest and electrical property maps would otherwise be expected to be most effective, not to mention most valuable for understanding tissue-field interactions that affect MR image quality and safety. It is also not known a priori precisely where and how the EPT approximation will break down for any particular body, opening up the possibility of unrecognized errors in property estimation.
Thus, there remains a need to provide apparatus, methods and computer-accessible mediums for noninvasive determination of electrical properties of tissues and materials.